Question

Juanita measures the angle of elevation from the ground to the top of an18-foot-tall tree as 30°. The image is of a tree whose height is 18 ft and its top is making an angle of 30 degrees with the ground. To the nearest tenth of a foot, how far is she from the tree?

Answer 1

As shown in the picture below she and the tree are making a 30-60-90 degree triangle. In the diagram, it is shown the bottom is sqrt(3)*x the side, so she is sqrt(3)*18 or 31.1769.

Answer 2

Juanita is standing 31.17 ft far from the tree.

Explanation:

Angle of elevation measured by Juanita =
`\theta=30^o`

Height of the tree = 18 ft

Also, an image of that tree whose height is 18 ft and its top is making an angle of 30°.This means length of the image is equal to the distance at which Juanita is standing.

In fig ΔABC

`(AB)/(BC)=\tan\theta`

`(18 ft)/(BC)=\tan 30^o=0.5773` (tan 30° = 0.5773)

BC = 31.17 ft ≈ 31.2 ft

Juanita is standing 31.2 ft far from the tree.